[B16] Primitive abelian period, character lattice, and global gauge form

[muellerberndt]

Determine the global form of the finite gauge action from the same source current and matter packet. The task must derive the primitive abelian period and full character lattice rather than assume U(1) normalization or infer the quotient from a desired Standard Model answer.

Deliverables:

• a source-derived primitive abelian generator and period;
• the complete character and cocharacter lattices of the selected finite matter action;
• exact source relations among the finite central elements;
• a loop-to-kernel theorem connecting B14 holonomy with the matter action;
• classification of the faithful global quotient on the declared finite module;
• controls for rescaled abelian generators, nonprimitive periods, incomplete matter spectra, and alternative central quotients;
• Lean theorems and deterministic certificates with an explicit assumption manifest.

A successful exit may establish a finite faithful global form such as the Standard Model quotient on the selected source module. It does not by itself identify a continuum gauge bundle, physical line operators, or laboratory gauge fields.

Absorbs the executable finite scope of archived #567.
Depends on: B14 (#705) and B15 (#706).
Wave: V2-W1 Observer laws.

[muellerberndt]

The target-clean lattice layer is computed (code/b16_lattices/, validator-replayed with three tamper modes failing closed): brackets rebuilt exactly at the certified generic samples with field towers, complete eigenspace decompositions, sl(2)-normalized coroots, and Cartan matrices computed as integer pairings; centers as Smith-normal-form lattice quotients giving the exact invariant factors. The finding: the certified twelve-port carrier decomposes as adjoint plus trivials in every compact family, every carrier weight lies in the root lattice, and the kernel of the center on the carrier is the whole center, so the source at carrier level selects the adjoint global form in all three families, with non-rigging controls showing one fundamental weight would drop the kernel to trivial and select the covering form. The primitive abelian period is proven undetermined at this level: every certified central generator acts by the exact zero matrix and the carrier charge lattice is zero, cross-pinned to the matter-class freeze. B16's remaining scope: the period, character lattice, and global form over a source-selected matter module from the frozen class, where the kernel computation is ready to rerun.